We have investigated multiple ionization of Xe clusters by 61-nm 1011–1012 W/cm2 extreme-ultraviolet light pulses at the free-electron laser facility, SPring-8 Compact SASE Source test accelerator, in Japan, using a dead-time-free three-dimensional momentum spectrometer. It was found that the average kinetic energy of atomic Xe+ ions increases when increasing the laser power density and the cluster size. For these experimental conditions significant frustration of the cluster photoionization occurs but no indication for heating mechanisms other than sequential photoabsorption by individual atoms in the cluster was found.